Classifying LEP Data with Support Vector Algorithms

We have studied the application of different classification algorithms in the analysis of simulated high energy physics data. Whereas Neural Network algorithms have become a standard tool for data analysis, the performance of other classifiers such as Support Vector Machines has not yet been tested in this environment. We chose two different problems to compare the performance of a Support Vector Machine and a Neural Net trained with back-propagation: tagging events of the type e+e- -> ccbar and the identification of muons produced in multihadronic e+e- annihilation events.Comment: 7 pages, 4 figures, submitted to proceedings of AIHENP99, Crete, April 199

Using Qubits to Measure Fidelity in Mesoscopic Systems

We point out the similarities in the definition of the `fidelity' of a quantum system and the generating function determining the full counting statistics of charge transport through a quantum wire and suggest to use flux- or charge qubits for their measurement. As an application we use the notion of fidelity within a first-quantized formalism in order to derive new results and insights on the generating function of the full counting statistics.Comment: 5 pages, 1 figur

Decoupling a Cooper-pair box to enhance the lifetime to 0.2 ms

We present a circuit QED experiment in which a separate transmission line is used to address a quasi-lumped element superconducting microwave resonator which is in turn coupled to an Al/AlO$_{x}$/Al Cooper-pair box (CPB) charge qubit. In our measurements we find a strong correlation between the measured lifetime of the CPB and the coupling between the qubit and the transmission line. By monitoring perturbations of the resonator's 5.44 GHz resonant frequency, we have measured the spectrum, lifetime ($T_{1}$), Rabi, and Ramsey oscillations of the CPB at the charge degeneracy point while the CPB was detuned by up to 2.5 GHz . We find a maximum lifetime of the CPB was $T_{1} = 200\ \mu$s for $f = 4$ to 4.5 GHz. Our measured $T_{1}$'s are consistent with loss due to coupling to the transmission line, spurious microwave circuit resonances, and a background decay rate on the order of $5\times 10^{3}$ s$^{-1}$ of unknown origin, implying that the loss tangent in the AlO$_{x}$ junction barrier must be less than about $4\times 10^{-8}$ at 4.5 GHz, about 4 orders of magnitude less than reported in larger area Al/AlO$_{x}$/Al tunnel junctions

High-Fidelity Readout in Circuit Quantum Electrodynamics Using the Jaynes-Cummings Nonlinearity

We demonstrate a qubit readout scheme that exploits the Jaynes-Cummings nonlinearity of a superconducting cavity coupled to transmon qubits. We find that in the strongly-driven dispersive regime of this system, there is the unexpected onset of a high-transmission "bright" state at a critical power which depends sensitively on the initial qubit state. A simple and robust measurement protocol exploiting this effect achieves a single-shot fidelity of 87% using a conventional sample design and experimental setup, and at least 61% fidelity to joint correlations of three qubits.Comment: 5 pages, 4 figure

Josephson Frequency Singularity in the Noise of Normal Metal-Superconductor Junctions

A singularity at the Josephson frequency in the noise spectral density of a disordered normal metal -- superconductor junction is predicted for bias voltages below the superconducting gap. The non-stationary Aharonov-Bohm effect, recently introduced for normal metals, is proposed as a tool for detecting this singularity. In the presence of a harmonic external field, the derivative of the noise with respect to the voltage bias reveals jumps when the applied frequency is commensurate with the Josephson frequency associated with this bias. The height of these jumps is non-monotonic in the amplitude of the periodic field. The superconducting flux quantum enters this dependence. Additional singularities in the frequency dependent noise are predicted above gap.Comment: 4 pages, 2 figures, revised versio

Comparing Support Vector Machines with Gaussian Kernels to Radial Basis Function Classifiers

The Support Vector (SV) machine is a novel type of learning machine, based on statistical learning theory, which contains polynomial classifiers, neural networks, and radial basis function (RBF) networks as special cases. In the RBF case, the SV algorithm automatically determines centers, weights and threshold such as to minimize an upper bound on the expected test error. The present study is devoted to an experimental comparison of these machines with a classical approach, where the centers are determined by $k$--means clustering and the weights are found using error backpropagation. We consider three machines, namely a classical RBF machine, an SV machine with Gaussian kernel, and a hybrid system with the centers determined by the SV method and the weights trained by error backpropagation. Our results show that on the US postal service database of handwritten digits, the SV machine achieves the highest test accuracy, followed by the hybrid approach. The SV approach is thus not only theoretically well--founded, but also superior in a practical application

Single-photon Resolved Cross-Kerr Interaction for Autonomous Stabilization of Photon-number States

Quantum states can be stabilized in the presence of intrinsic and environmental losses by either applying active feedback conditioned on an ancillary system or through reservoir engineering. Reservoir engineering maintains a desired quantum state through a combination of drives and designed entropy evacuation. We propose and implement a quantum reservoir engineering protocol that stabilizes Fock states in a microwave cavity. This protocol is realized with a circuit quantum electrodynamics platform where a Josephson junction provides direct, nonlinear coupling between two superconducting waveguide cavities. The nonlinear coupling results in a single photon resolved cross-Kerr effect between the two cavities enabling a photon number dependent coupling to a lossy environment. The quantum state of the microwave cavity is discussed in terms of a net polarization and is analyzed by a measurement of its steady state Wigner function.Comment: 8 pages, 6 figure

Proposal for generating and detecting multi-qubit GHZ states in circuit QED

We propose methods for the preparation and entanglement detection of multi-qubit GHZ states in circuit quantum electrodynamics. Using quantum trajectory simulations appropriate for the situation of a weak continuous measurement, we show that the joint dispersive readout of several qubits can be utilized for the probabilistic production of high-fidelity GHZ states. When employing a nonlinear filter on the recorded homodyne signal, the selected states are found to exhibit values of the Bell-Mermin operator exceeding 2 under realistic conditions. We discuss the potential of the dispersive readout to demonstrate a violation of the Mermin bound, and present a measurement scheme avoiding the necessity for full detector tomography.Comment: 9 pages, 5 figure